Le 26/08/2012 11:42, Martin Ennemoser a écrit : > Hi Luc! > > Thank you for your answer. I tried it an it works. But isn't there an easier > way to build a polyhedron? Do I relly need this projection and line stuff?
I think some of these steps could be gathered in a utility method, but we didn't do it. Patches are welcome! One should be aware of the facets orientation, so it may be difficult to set up a robust method though. Another way to build polyhedrons is to use the basic constructive geometry operations (union, intersection, difference, symmetric difference, complement ...). best regards, Luc > > Best regards, > > Martin > > -------- Original-Nachricht -------- >> Datum: Sat, 25 Aug 2012 14:03:33 +0200 >> Von: Luc Maisonobe <luc.maison...@free.fr> >> An: Commons Users List <user@commons.apache.org> >> Betreff: Re: [math] How to use the BSP Tree? > >> Le 25/08/2012 12:17, Martin Ennemoser a écrit : >>> Hi! >> >> Hi Martin, >> >>> >>> I have a polyhedron in 3D space that consists of a triangle mesh. Now I >> want to use the BSP tree to classify wheter a point is inside or outside of >> the polyhedron. >>> The problem is that I don't know how to construct a BSP tree with my >> polyhedron vertices. The user guide only gives provides little information. >>> Maybe someone could give me with a short code example. >> >> You can look for example at the junit tests. One example is testIssue780 >> in the PolyhedronsSetTest class in package >> org.apache.commons.math3.geometry.euclidean.threed. The algorithm used >> by the test is the following: >> >> 1) set up the points coordinates for all vertices of the polyhedron >> 2) set up the mesh triangles by using an indirection array >> of indices (i.e. somthing like triangle 1 uses points 1, 2 and 3, >> triangle 2 uses point 4, 5 and 1, traingle 3 uses ...) >> 3) for each triangle, create a facet using the following stages: >> 3a) create a 3D plane from the three points >> 3b) create 2D points by projecting the 3D points into the plane >> 3c) create three 2D lines by joining all pairs of projected 3D points >> 3c) create a 2D PolygonSet using the 2D lines >> 3d) create a 3D SubPlane using the plane and the 2D PolygonSet >> 4) create the PolyhedronSet using all 3D SubPlanes >> >> The main trick is the 2D/3D projection that occurs at each facet. >> >> Beware that when you create a Region from a collection of boundary >> elements (i.e. creating a PolygonSet from lines or creating a >> PolyhedronSet from facets), the elements in the boundary must be >> oriented, as they define which half space will be the interior and which >> half space will be the exterior. The convention we use is that the >> interior is on the minus side of the hyperplane. For lines, the plus >> side is the half space on the right when traveling along the line in >> ascending coordinate direction. This implies that if you define a square >> polygon, you should define the boundary in counterclockwise direction if >> you want the interior to be the finite square (on the left as you travel >> in counterclockwise direction along the boundary) and the exterior to be >> the infinite plane minus the central square (on the right as you travel >> in counterclockwise direction along the boundary). If you define the >> boundary in the opposite direction (i.e clockwise), the interior will be >> the infinite region and the exterior will be the finite square. If you >> define your boundary with some elements in one direction and other >> elements in the opposite direction, this will fail. For planes in 3D, >> the plus half space is towards plane normal. >> >> best regards, >> Luc >> >>> >>> Thank you! >>> >>> --------------------------------------------------------------------- >>> To unsubscribe, e-mail: user-unsubscr...@commons.apache.org >>> For additional commands, e-mail: user-h...@commons.apache.org >>> >>> >> >> >> --------------------------------------------------------------------- >> To unsubscribe, e-mail: user-unsubscr...@commons.apache.org >> For additional commands, e-mail: user-h...@commons.apache.org >> > > --------------------------------------------------------------------- > To unsubscribe, e-mail: user-unsubscr...@commons.apache.org > For additional commands, e-mail: user-h...@commons.apache.org > > --------------------------------------------------------------------- To unsubscribe, e-mail: user-unsubscr...@commons.apache.org For additional commands, e-mail: user-h...@commons.apache.org
